Section 8-2 Union, Intersection, and Complement of Events Example 1



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Section 8-2 Union, Intersection, and Complement of Events
Example 1
From a survey involving 1,000 students, a market research company found that 750 students owned stereos, 450 owned cars, and 350 owned both. What is the probability that a student selected at random does not own a car? Owns a car but not a stereo?
Given: n(Survey) = 1000, n(Stereo) = 750, n(Car) = 450, n(Stereo ∩ Car) = 350
Venn Diagram

P(Car’) = 1 – P(Car)

= 1 – 0.450

= 0.550
P(Car ∩ Stereo′) = 0.100


We can also use probability trees to find the probabilities. Notice that we get the same result whether we use the first column for cars or for stereos:

Example 2
In order to test a new car, an automobile manufacturer wants to select 4 employees to test drive the car for one year. If 12 management and 8 union employees volunteer to be test drivers and the selection is made at random, what is the probability that at least 1 union employee is selected?
The sample space is the set of all possible sets of 4 drivers taken from these 20 volunteers.

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